Prosper Loans Exploration by Krasin Georgiev
Univariate Plots Section
| Term | LoanOriginalAmount | BorrowerAPR | LenderYield | EstimatedLoss | LoanStatus |
|---|---|---|---|---|---|
| 36 | 9425 | 0.16516 | 0.1380 | NA | Completed |
| 36 | 10000 | 0.12016 | 0.0820 | 0.0249 | Current |
| 36 | 3001 | 0.28269 | 0.2400 | NA | Completed |
| 36 | 10000 | 0.12528 | 0.0874 | 0.0249 | Current |
| 36 | 15000 | 0.24614 | 0.1985 | 0.0925 | Current |
| 60 | 15000 | 0.15425 | 0.1214 | 0.0449 | Current |
## [1] "Term" "LoanStatus"
## [3] "ClosedDate" "BorrowerAPR"
## [5] "BorrowerRate" "LenderYield"
## [7] "EstimatedLoss" "EstimatedReturn"
## [9] "ProsperRating..Alpha." "ProsperScore"
## [11] "EmploymentStatus" "EmploymentStatusDuration"
## [13] "IsBorrowerHomeowner" "CreditScoreRangeLower"
## [15] "CreditScoreRangeUpper" "DelinquenciesLast7Years"
## [17] "DebtToIncomeRatio" "IncomeRange"
## [19] "StatedMonthlyIncome" "LoanOriginalAmount"
## [21] "Date" "MonthlyLoanPayment"
## [23] "Recommendations" "Year"## Term LoanStatus
## Min. :12.00 Current :56576
## 1st Qu.:36.00 Completed :38074
## Median :36.00 Chargedoff :11992
## Mean :40.83 Defaulted : 5018
## 3rd Qu.:36.00 Past Due (1-15 days) : 806
## Max. :60.00 Past Due (31-60 days): 363
## (Other) : 1108
## ClosedDate BorrowerAPR BorrowerRate
## Min. :2005-11-25 00:00:00 Min. :0.00653 Min. :0.0000
## 1st Qu.:2009-07-14 00:00:00 1st Qu.:0.15629 1st Qu.:0.1340
## Median :2011-04-05 00:00:00 Median :0.20976 Median :0.1840
## Mean :2011-03-07 19:48:20 Mean :0.21883 Mean :0.1928
## 3rd Qu.:2013-01-30 00:00:00 3rd Qu.:0.28381 3rd Qu.:0.2500
## Max. :2014-03-10 00:00:00 Max. :0.51229 Max. :0.4975
## NA's :58848 NA's :25
## LenderYield EstimatedLoss EstimatedReturn ProsperRating..Alpha.
## Min. :-0.0100 Min. :0.005 Min. :-0.183 C :18345
## 1st Qu.: 0.1242 1st Qu.:0.042 1st Qu.: 0.074 B :15581
## Median : 0.1730 Median :0.072 Median : 0.092 A :14551
## Mean : 0.1827 Mean :0.080 Mean : 0.096 D :14274
## 3rd Qu.: 0.2400 3rd Qu.:0.112 3rd Qu.: 0.117 E : 9795
## Max. : 0.4925 Max. :0.366 Max. : 0.284 (Other):12307
## NA's :29084 NA's :29084 NA's :29084
## ProsperScore EmploymentStatus EmploymentStatusDuration
## Min. : 1.00 Employed :67322 Min. : 0.00
## 1st Qu.: 4.00 Full-time :26355 1st Qu.: 26.00
## Median : 6.00 Self-employed: 6134 Median : 67.00
## Mean : 5.95 Not available: 5347 Mean : 96.07
## 3rd Qu.: 8.00 Other : 3806 3rd Qu.:137.00
## Max. :11.00 : 2255 Max. :755.00
## NA's :29084 (Other) : 2718 NA's :7625
## IsBorrowerHomeowner CreditScoreRangeLower CreditScoreRangeUpper
## False:56459 Min. : 0.0 Min. : 19.0
## True :57478 1st Qu.:660.0 1st Qu.:679.0
## Median :680.0 Median :699.0
## Mean :685.6 Mean :704.6
## 3rd Qu.:720.0 3rd Qu.:739.0
## Max. :880.0 Max. :899.0
## NA's :591 NA's :591
## DelinquenciesLast7Years DebtToIncomeRatio IncomeRange
## Min. : 0.000 Min. : 0.000 $25,000-49,999:32192
## 1st Qu.: 0.000 1st Qu.: 0.140 $50,000-74,999:31050
## Median : 0.000 Median : 0.220 $100,000+ :17337
## Mean : 4.155 Mean : 0.276 $75,000-99,999:16916
## 3rd Qu.: 3.000 3rd Qu.: 0.320 Not displayed : 7741
## Max. :99.000 Max. :10.010 $1-24,999 : 7274
## NA's :990 NA's :8554 (Other) : 1427
## StatedMonthlyIncome LoanOriginalAmount Date
## Min. : 0 Min. : 1000 Min. :2005-11-15 00:00:00
## 1st Qu.: 3200 1st Qu.: 4000 1st Qu.:2008-10-02 00:00:00
## Median : 4667 Median : 6500 Median :2012-06-26 00:00:00
## Mean : 5608 Mean : 8337 Mean :2011-07-21 03:44:57
## 3rd Qu.: 6825 3rd Qu.:12000 3rd Qu.:2013-09-18 00:00:00
## Max. :1750003 Max. :35000 Max. :2014-03-12 00:00:00
##
## MonthlyLoanPayment Recommendations Year
## Min. : 0.0 Min. : 0.00000 Min. :2005
## 1st Qu.: 131.6 1st Qu.: 0.00000 1st Qu.:2008
## Median : 217.7 Median : 0.00000 Median :2012
## Mean : 272.5 Mean : 0.04803 Mean :2011
## 3rd Qu.: 371.6 3rd Qu.: 0.00000 3rd Qu.:2013
## Max. :2251.5 Max. :39.00000 Max. :2014
## Loans vary from $1000 to $35000. The monthly loan payment is from $130 to $2250.
The average cost for the borrower (BorrowerAPR) is 21.9%, the average yield for the lender (LenderYield) is 18.2%. Considering that the estimated loss for the lender is 8 %, the return is actually 9.6% on average. These numbers vary quite widely - the return can be actually negative (minimal value at -18.3%) and in 50% of all cases is between 7.4% and 11%. So it will be interesting to see the distribution of borrower costs and investors profit. For the borrower the range is (0.00653, 0.51229).
The distributions of Interest rate look similar in both cases, widely spread. Lenderers yield is squeezed and shifted to the left relative to the borrower APR. There is strange peak close to the maximum values. The lenders estimated return is also multimodal distribution with strange peaks.
There is a difference between client interest rate (BorrowerAPR) and investor interest rate (LenderYield). In order to explore the profit for Prosper we create a new variable ProsperReturn.
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 0.00069 0.03110 0.03531 0.03610 0.04655 0.15940 25
The average Prosper profit is 3.6% of all loans per year. From the histogram it is visible that values are clustered arround several points.
There are only 3 options for loan period - 1, 3 and 5 years:
##
## 12 36 60
## 1614 87778 24545The following plot will visualize the distribution of the amounts loaned:
Loan ammounts in most cases take discrete values, e.g. 4000, 10000, 15000, 20000. The highest peak is for $4000.
Next we explore the final state or the loan status. Because there are only few records wih status “Cancelled” we will remove them. Then “Completed” and “FinalPaymentInProgress” are merged in single level. Possible states are ordered in a logical way. In another variable LoanStatusShort all “Past due” above 15 days are merged.
## [1] "Cancelled" "Chargedoff"
## [3] "Completed" "Current"
## [5] "Defaulted" "FinalPaymentInProgress"
## [7] "Past Due (1-15 days)" "Past Due (>120 days)"
## [9] "Past Due (16-30 days)" "Past Due (31-60 days)"
## [11] "Past Due (61-90 days)" "Past Due (91-120 days)"## [1] 5
##
## Completed Current Past Due (1-15 days)
## 38279 56576 806
## Past Due (16-30 days) Past Due (31-60 days) Past Due (61-90 days)
## 265 363 313
## Past Due (91-120 days) Past Due (>120 days) Defaulted
## 304 16 5018
## Chargedoff
## 11992##
## Completed Current Past Due (1-15 days)
## 38279 56576 806
## Past Due (>15 days) Defaulted Chargedoff
## 1261 5018 11992We can see that most loans from our dataset are still current. In order to get idea for the risk of failed payments we will consider only the loans that should have been completed:
##
## Completed Current Past Due (1-15 days)
## 65.6511822 4.3711892 0.1798482
## Past Due (>15 days) Defaulted Chargedoff
## 0.2412598 9.9245515 19.6319691About 65.6% of past loans are completed on time. The rest are charged-off, defaulted or extended (still current).
The number of Prosper loans by year is as follows:
##
## 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014
## 22 5902 11460 11551 2047 5652 11228 19553 34345 12172Most of the loans are still to be completed (these are loans for which the planned completion date is after the last dataset update date):
table(loans$PlannedClosing > last_updated)##
## FALSE TRUE
## 45649 68283The risk of the loan is expressed as Prosper Rating:
Another measure of the risk is Prosper Score:
and credit score:
Debt to income ratio is:
## Warning in scale$trans$trans(x): NaNs produced
##
## 0.18 0.22 0.17 0.14 0.2 0.16 0.19 0.15 0.21 0.13
## 4132 3687 3616 3553 3481 3442 3392 3338 3226 3169It looks nearly normally distributed on square axes x.
Univariate Analysis
What is the structure of your dataset?
There are 113932 loans in the dataset with 81 features, including loan amount, borrower rate (or interest rate), current loan status, borrower income, borrower employment status, borrower credit history, and the latest payment information. More information on variables in the data set is available at Prosper website Dataset is last updated on 03/11/2014.
What is/are the main feature(s) of interest in your dataset?
The main features for the loans dataset are as follows:
BorrowerAPR- the cost of credit as a yearly rate for the borrower. The borrower’s interest rate plus closing fee distrubuted in time;LenderYield- The Lender yield on the loan. The borrower’s interest rate less the lender servicing fee.EstimatedReturn\(\approx LenderYield - EstimatedLoss\) Estimated Loss RatesLoanStatus- The current status of the loan. Past data about the possible final states completed and charged of could be used to calculate actual loss rates.
What other features in the dataset do you think will help support your investigation into your feature(s) of interest?
These are some of features that determine the main features or give details about the loan.
LoanOriginalAmount- The origination amount of the loan.Term- The length of the loan expressed in months.ClosedDate- Closed date is applicable for Cancelled, Completed, Chargedoff and Defaulted loan statuses.ProsperRating..Alpha.,ProsperScore,CreditScoreRangeLower,CreditScoreRangeUpper: Used to calculate Estimated LossDelinquenciesLast7Years- The number of times the borrower has been more than 90 days late with a payment.DebtToIncomeRatio- he sum of the borrower’s monthly debt payments divided by the borrower’s monthly income.IncomeRange,StatedMonthlyIncome- yearly income group and monthly income.IsBorrowerHomeownerEmploymentStatus,EmploymentStatusDuration
These variables are of different types, e.g. date (LoanOriginationDate), ordered factors (ProsperRating..Alpha., IncomeRange), categorical factor (EmploymentStatus, LoanStatus, Occupation), binary (IsBorrowerHomeowner). There are also sparse variables (mostly zeroes): Recommendations.
Did you create any new variables from existing variables in the dataset?
In order to estimate Prosper yield I created \(ProsperYield = BorrowerAPR - LenderYield\)
To explore the changes of the main variables in time I converted LoanOriginalAmount to date type and then extracted the year as new variable loans$Year.
The planned closing date was estimated as a sum of date of loan start and loan duration. It is used to subset only past loans that should be closed.
Of the features you investigated, were there any unusual distributions? Did you perform any operations on the data to tidy, adjust, or change the form of the data? If so, why did you do this?
On Prosper profit histogram the values are clustered arround several points.
There is a strange peak in Interest rate histograms.
Prosper rating and Prosper score have quite a few missing values.
Date strings were converted to dates so they can be properly plotted, subtracted and compared. Some categorical variables were converted to ordered factors for better plotting.
LoanStatus was modified to so that “FinalPaymentInProgress” is replaced by “Completed”. Records with LoanStatus equal to “Canceled” were removed from the dataset, as not important for the analysis.
Bivariate Plots Section
We can review the linear relationship between numerical variables:
## BorrowerAPR BorrowerRate LenderYield
## BorrowerAPR 1.00000000 0.98982516 0.98933059
## BorrowerRate 0.98982516 1.00000000 0.99921140
## LenderYield 0.98933059 0.99921140 1.00000000
## EstimatedLoss 0.94953750 0.94529698 0.94530836
## EstimatedReturn 0.79427520 0.81766987 0.81765407
## ProsperScore -0.66828720 -0.64973614 -0.64978347
## EmploymentStatusDuration -0.00859336 -0.01991508 -0.01896211
## CreditScoreRangeLower -0.42971905 -0.46157312 -0.45435242
## CreditScoreRangeUpper -0.42971905 -0.46157312 -0.45435242
## DelinquenciesLast7Years 0.16222249 0.17027647 0.16799777
## DebtToIncomeRatio 0.05633133 0.06292314 0.06194961
## StatedMonthlyIncome -0.08233918 -0.08898236 -0.08820745
## LoanOriginalAmount -0.32290338 -0.32897643 -0.32846928
## MonthlyLoanPayment -0.22666716 -0.24475674 -0.24422614
## Year 0.06488217 -0.02877050 -0.02769339
## ProsperReturn 0.52256948 0.40050505 0.39278087
## EstimatedLoss EstimatedReturn ProsperScore
## BorrowerAPR 0.94953750 0.79427520 -0.668287197
## BorrowerRate 0.94529698 0.81766987 -0.649736144
## LenderYield 0.94530836 0.81765407 -0.649783473
## EstimatedLoss 1.00000000 0.59105567 -0.673726990
## EstimatedReturn 0.59105567 1.00000000 -0.383210592
## ProsperScore -0.67372699 -0.38321059 1.000000000
## EmploymentStatusDuration -0.03916047 -0.03648651 -0.007302109
## CreditScoreRangeLower -0.51126282 -0.34623273 0.369603047
## CreditScoreRangeUpper -0.51126282 -0.34623273 0.369603047
## DelinquenciesLast7Years 0.14390563 0.09443582 -0.097754738
## DebtToIncomeRatio 0.12611550 0.08723617 -0.145335892
## StatedMonthlyIncome -0.08925850 -0.07501281 0.083756653
## LoanOriginalAmount -0.42989040 -0.28611751 0.266293336
## MonthlyLoanPayment -0.32870274 -0.25273127 0.175424879
## Year -0.20819220 -0.37647287 -0.169729188
## ProsperReturn 0.51457769 0.23663444 -0.473959705
## EmploymentStatusDuration CreditScoreRangeLower
## BorrowerAPR -0.008593360 -0.42971905
## BorrowerRate -0.019915084 -0.46157312
## LenderYield -0.018962110 -0.45435242
## EstimatedLoss -0.039160473 -0.51126282
## EstimatedReturn -0.036486506 -0.34623273
## ProsperScore -0.007302109 0.36960305
## EmploymentStatusDuration 1.000000000 0.08113775
## CreditScoreRangeLower 0.081137748 1.00000000
## CreditScoreRangeUpper 0.081137748 1.00000000
## DelinquenciesLast7Years 0.012220125 -0.25122258
## DebtToIncomeRatio -0.011608411 -0.01319115
## StatedMonthlyIncome 0.069827805 0.10788271
## LoanOriginalAmount 0.098142303 0.34084904
## MonthlyLoanPayment 0.081152542 0.29250135
## Year 0.168495113 0.33364308
## ProsperReturn 0.060590672 -0.05340718
## CreditScoreRangeUpper DelinquenciesLast7Years
## BorrowerAPR -0.42971905 0.16222249
## BorrowerRate -0.46157312 0.17027647
## LenderYield -0.45435242 0.16799777
## EstimatedLoss -0.51126282 0.14390563
## EstimatedReturn -0.34623273 0.09443582
## ProsperScore 0.36960305 -0.09775474
## EmploymentStatusDuration 0.08113775 0.01222013
## CreditScoreRangeLower 1.00000000 -0.25122258
## CreditScoreRangeUpper 1.00000000 -0.25122258
## DelinquenciesLast7Years -0.25122258 1.00000000
## DebtToIncomeRatio -0.01319115 -0.04387708
## StatedMonthlyIncome 0.10788271 -0.02580636
## LoanOriginalAmount 0.34084904 -0.13667279
## MonthlyLoanPayment 0.29250135 -0.12125278
## Year 0.33364308 -0.08304944
## ProsperReturn -0.05340718 0.04102281
## DebtToIncomeRatio StatedMonthlyIncome
## BorrowerAPR 0.056331332 -0.082339182
## BorrowerRate 0.062923138 -0.088982364
## LenderYield 0.061949612 -0.088207454
## EstimatedLoss 0.126115503 -0.089258503
## EstimatedReturn 0.087236166 -0.075012815
## ProsperScore -0.145335892 0.083756653
## EmploymentStatusDuration -0.011608411 0.069827805
## CreditScoreRangeLower -0.013191145 0.107882708
## CreditScoreRangeUpper -0.013191145 0.107882708
## DelinquenciesLast7Years -0.043877077 -0.025806361
## DebtToIncomeRatio 1.000000000 -0.122667527
## StatedMonthlyIncome -0.122667527 1.000000000
## LoanOriginalAmount 0.010102221 0.201245819
## MonthlyLoanPayment 0.027588782 0.196816155
## Year -0.044196692 0.080847424
## ProsperReturn -0.006624287 -0.004232326
## LoanOriginalAmount MonthlyLoanPayment Year
## BorrowerAPR -0.32290338 -0.2266671612 0.06488217
## BorrowerRate -0.32897643 -0.2447567413 -0.02877050
## LenderYield -0.32846928 -0.2442261368 -0.02769339
## EstimatedLoss -0.42989040 -0.3287027419 -0.20819220
## EstimatedReturn -0.28611751 -0.2527312679 -0.37647287
## ProsperScore 0.26629334 0.1754248787 -0.16972919
## EmploymentStatusDuration 0.09814230 0.0811525418 0.16849511
## CreditScoreRangeLower 0.34084904 0.2925013466 0.33364308
## CreditScoreRangeUpper 0.34084904 0.2925013466 0.33364308
## DelinquenciesLast7Years -0.13667279 -0.1212527803 -0.08304944
## DebtToIncomeRatio 0.01010222 0.0275887822 -0.04419669
## StatedMonthlyIncome 0.20124582 0.1968161546 0.08084742
## LoanOriginalAmount 1.00000000 0.9319801778 0.31068458
## MonthlyLoanPayment 0.93198018 1.0000000000 0.25812364
## Year 0.31068458 0.2581236399 1.00000000
## ProsperReturn -0.11404694 0.0005283696 0.57588654
## ProsperReturn
## BorrowerAPR 0.5225694781
## BorrowerRate 0.4005050528
## LenderYield 0.3927808695
## EstimatedLoss 0.5145776863
## EstimatedReturn 0.2366344355
## ProsperScore -0.4739597052
## EmploymentStatusDuration 0.0605906718
## CreditScoreRangeLower -0.0534071846
## CreditScoreRangeUpper -0.0534071846
## DelinquenciesLast7Years 0.0410228051
## DebtToIncomeRatio -0.0066242871
## StatedMonthlyIncome -0.0042323257
## LoanOriginalAmount -0.1140469395
## MonthlyLoanPayment 0.0005283696
## Year 0.5758865395
## ProsperReturn 1.0000000000## [1] 0.8745126Some of the variables have subtle differences, e.g. BorrowerAPR, BorrowerRate, LenderYield (corr. coef 0.99). In other cases stronger correlation shows important connections: BorrowerAPR is linked to ProsperScore (-0.67) and CreditScoreRangeLower (-0.43).
The relationship between Loan status and close date:
##
## FALSE TRUE
## Completed 205 38074
## Current 56576 0
## Past Due (1-15 days) 806 0
## Past Due (16-30 days) 265 0
## Past Due (31-60 days) 363 0
## Past Due (61-90 days) 313 0
## Past Due (91-120 days) 304 0
## Past Due (>120 days) 16 0
## Defaulted 0 5018
## Chargedoff 0 11992Close date is available for Completed, Chargedoff and Defaulted loans.
I would like to calculate the actual loss rate of past loans. I will start by exploring available risk indicators. The next explanation is quotation from Prosper website:
The estimated loss rate is based on the historical performance of Prosper loans with similar characteristics. The estimated base loss rate is determined by two scores: (1) the borrower’s credit score, obtained from an official credit reporting agency, and (2) the Prosper Score, figured in-house based on the Prosper population. These two scores determine the base loss rate for each listing. Adjustments can then be made to the base loss rate for the presence of a previous Prosper loan and for certain loan terms. Any adjustments are added to the base loss rate to get the final loss rate, which then determines the Prosper Rating.
So, Prosper rating and Prosper score are related:
##
## AA A B C D E HR
## 1 0 2 3 21 49 552 365
## 2 0 6 61 490 1255 2692 1262
## 3 4 53 367 1711 2295 1750 1462
## 4 14 285 1451 4738 2506 1681 1920
## 5 11 608 1695 2642 1940 1262 1655
## 6 94 1392 2968 2900 3256 1438 230
## 7 164 2050 2624 3370 2251 118 20
## 8 718 4170 4781 1482 679 214 9
## 9 983 4070 968 770 36 75 9
## 10 2645 1394 492 196 7 13 3
## 11 739 521 171 25 0 0 0## Warning: Removed 29079 rows containing non-finite values (stat_boxplot).## Warning: Removed 29079 rows containing missing values (geom_point).
It is strange that the worst Prosper rating does not have the lowest Prosper scores.
The Prosper rating vs Year:
##
## AA A B C D E HR
## 2005 0 0 0 0 0 0 0
## 2006 0 0 0 0 0 0 0
## 2007 0 0 0 0 0 0 0
## 2008 0 0 0 0 0 0 0
## 2009 297 458 98 390 333 193 207
## 2010 639 963 536 594 1311 630 906
## 2011 551 1479 1610 888 3273 2306 1121
## 2012 1076 2760 3071 3891 3222 1904 3629
## 2013 1721 5943 7558 9223 5017 3914 969
## 2014 1088 2948 2708 3359 1118 848 103##
## FALSE TRUE
## 2005 0 22
## 2006 0 5902
## 2007 0 11460
## 2008 0 11551
## 2009 1976 71
## 2010 5579 73
## 2011 11228 0
## 2012 19553 0
## 2013 34345 0
## 2014 12172 0
Prosper rating is introduced in 2009. Starting from 2011 all records have assigned Prosper rating. Comparing the distributions of loans by Prosper rating for early years and last years we see that they are quite different (flat vs “bell” shape). Therefore our conclusions based on past data will not be very representative of the current situation.
Separate subset of past loans but without missing ProsperRating is created.
## [1] 16515The link between “EstimatedLoss” and “ProsperRating..Alpha.” is visualized:
## [1] "Correlation between estimated loss and Prosper rating:"## [1] 0.9641819## [1] "Correlation between estimated loss and Prosper rating for past loans:"## [1] 0.9396867It is quite straitforward. Only “HR” rating has quite dispersed values.
If we compare the loan closing date with the planned closing we will be surprised: We have early repayment in 76% of all cases:
##
## FALSE TRUE
## 0.2338358 0.7608088## Warning: Removed 205 rows containing missing values (geom_point).
The link between Prosper Rating and Loan status will be explored for past loans.
## IsCompleted
## ProsperRating..Alpha. FALSE TRUE
## AA 125 1293
## A 514 2012
## B 474 1318
## C 443 1425
## D 1401 2671
## E 1275 1633
## HR 760 1171
The performance of loans with rating “A”, “B” and “C” look very similar. Loans “D”, “E” and “HR” are also similar considering completion status, with rating “HR” having higher completion ratio than “E”.
This can imply that borrowers with Prosper rating “C” should be prefered against “A”, “B” and that “HR” are better than “D”, “E”. Further exploration considering the actual amount lost for uncompleted loans worth exploration.
Prosper return is lower and less dispersed for longer duration loans.
## [1] 0.2408804## [1] -0.1920841The relationship of completed loans with credit score is much smooter than with Lender Yield and Estimated Loss. Therefore other factors except from risk level shape the interest rate for the lender. This means also that Credit Score is better measure for borrower reliability than the Estimated Loss.
## Warning: Removed 29079 rows containing missing values (stat_summary).## Warning: Removed 29079 rows containing missing values (geom_point).
## Warning: Removed 29274 rows containing missing values (stat_summary).## Warning: Removed 29275 rows containing missing values (geom_point).
Next, changes in lender yield are cosidered in time:
In last four years (2011 to 2014) there is continuous reduction in lenders yield. Also, lander yield looks quite different in different years. The period of no Prosper activity is also visible.
## Warning: Removed 25 rows containing non-finite values (stat_boxplot).## Warning: Removed 25 rows containing missing values (geom_point).
At the same time Prosper profit is quite stable.
Looking at the return based on loan original amount does not reveal interesting insights.
## geom_smooth: method="auto" and size of largest group is >=1000, so using gam with formula: y ~ s(x, bs = "cs"). Use 'method = x' to change the smoothing method.## Warning: Removed 29079 rows containing missing values (stat_smooth).## Warning: Removed 29079 rows containing missing values (geom_point).
There are more loans of small amounts and higher dispersion of the return.
Bivariate Analysis
Talk about some of the relationships you observed in this part of the investigation. How did the feature(s) of interest vary with other features in the dataset?
We concluded that estimated loss is closely related to Prosper Rating.
The relationship between the proportion of completed loans and Credit Score is stronger than to Prosper Rating or Estimated Loss.
Estimated return is related to estimated loss. The relationship is not linear and there is optimal estimated loss for maximal return.
Did you observe any interesting relationships between the other features (not the main feature(s) of interest)?
The most interesting insight is that big part (76%) of the completed loans are repayed in advance, before the planned closing date.
What was the strongest relationship you found?
Correlation between estimated loss and Prosper rating: 0.96.
Multivariate Plots Section
Lender Yield and Return are presented on the same plot so that the effect on the profit of higher risk loans with higher interest is clear. Only the mean value and 0.05, 0.5 and 0.95 quantiles will be presented to show the general trend and uncertainty level.
There is optimum between losses 0.1 and 0.2. At higher losses there is jump in uncertainty.
Next, changes in lender yield are considered in time:
The same for prosper return:
## Warning: Removed 25 rows containing missing values (geom_point).
## Warning: Removed 25 rows containing missing values (stat_smooth).
## Warning: Removed 4158 rows containing missing values (geom_point).
The relationship between monthly income, credit score and isCompleted - nothing special!
Multivariate Analysis
Talk about some of the relationships you observed in this part of the investigation. Were there features that strengthened each other in terms of looking at your feature(s) of interest?
Lender Yield and Return are presented on the same plot as a function of estimated loss. Above losses 0.2 lender yield stop to increase and lender return drops sharply. At higher losses there is jump in uncertainty.
Lenders Yield is reduced in years. This become more clear when loans are divided by Prosper rating. On the contrary, Prosper Return is increasing.
Were there any interesting or surprising interactions between features?
Several different periods in Prosper loan data can be identified with jump change of loan properties (e.g. see LendersYield vs Date). Therefore most of the conclusion in this report should be treated with causion.
OPTIONAL: Did you create any models with your dataset? Discuss the strengths and limitations of your model.
A model exploring how different features influence IsCompleted variable for past loans can be used to fine tune risk measure variables (e.g. ProsperRating).
Final Plots and Summary
Plot One - the link between Prosper Rating and Loan status for past loans
Description One
Based on past loans we calculate the proportion of uncompleted loans based on different risk measures - Prosper Rating, Estimated losses and Credit Score.
The relationship of completed loans with credit score is much smooter than with Lender Yield and Estimated Loss. Looks like Credit Score is better measure for borrower reliability than the Estimated Loss and Prosper Rating.
Prosper rating is important because it determines the Interest rate. The performance of loans with rating “A”, “B” and “C” look very similar. Loans “D”, “E” and “HR” are also similar considering completion status, with rating “HR” having higher completion ratio than “E”. This can imply that borrowers with Prosper rating “C” should be prefered against “A”, “B” and that “HR” are better than “D”, “E”.
Further exploration considering the actual amount lost for uncompleted loans worth exploration.
Plot Two
Description Two
Both lender yield (interest rate) and return are presented as a function of lender estimated loss. Because at the same estimated loss different interests are possible, mean value and [0.05, 0.5, 0.95] quantiles are presented.
Up to 15% loss both yield and return are increasing. Then yield become constant but the return start to drop. Therefore, there is a kind of optimal risk acceptance level for highest profit. Both low and high losses have low return, but high losses can lead even to negative return.
Uncertainty become much higher at estimate loss above 25%. There is wide margine in negative direction.
Plot Three
## Warning: Removed 205 rows containing missing values (geom_point).
Description Three
Early repayment is typical situation. All points below the diagonal bolder line are preliminary payments. ——
Reflection
Two datasets were used for this analysis. One is the original full dataset. It is used to calculate the relationship between the primary parameters, like lenders return vs estimated loss.
The other dataset containes only past records that should have expired. For this past data we have the information whether the loan have been completed (or Chargedoff-ed). It is used to check the effectiveness of different risk measures. We noticed that 35% the past loans have not been completed in terms. The best measure of the risk is Credit Score. Prosper ratings “C” and “HR” should be preferred for lenders with lower and higher tolerance to risk.
It will be usefull to continue the exploration by calculating what part of the total amount is lost for uncompleted loans and how it differes for different borrower categories.
The biggest problem was that the main feature of interest - the actual return is not available and should be estimated somehow. This is complicated by the enormous number of features. Specialized feature selection algorithms could be important to guide the analysis.
NOTE: Our conclusions are based on past data and will not be very representative of the current situation because the Prosper system is changing in years.
Working with dates created some technical difficulties. Some methods and operations result into POSIXlt date, other in POSIXct. Trying to compare them throws error. Mastering the fine differences between strptime, strftime, as.Date, as.POSIXct, as.difftime could be challenging.